OpenRaiser/Intern-Atlas huggingface dataset:
Multilevel Polarization of Polar Codes Over Arbitrary Discrete Memoryless Channels
Venue: arXiv cs.IT 2012
Year: 2012

It is shown that polar codes achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the synthesized channels are either useless, perfect or "partially perfect". Any subset of the channel input alphabet which is closed under addition, induces a coset partition of the alphabet through its shifts. For any such partition of the input alphabet, there exists a corresponding partially perfect channel whose outputs uniquely determine the coset to which the channel input belongs. By a slight modification of the encoding and decoding rules, it is shown that perfect transmission of certain information symbols over partially perfect channels is possible. Our result is general regarding both the cardinality and the algebraic structure of the channel input alphabet; i.e we show that for any channel input alphabet size and any Abelian group structure on the alphabet, polar codes are optimal. It is also shown through an example that polar codes when considered as group/coset codes, do not achieve the capacity achievable using coset codes over arbitrary channels.
An Interpretation of the Moore-Penrose Generalized Inverse of a Singular Fisher Information Matrix
Venue: arXiv cs.IT 2012
Year: 2012

It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramer-Rao bound (CRB), a popular tool to lower bound the variances of unbiased estimators, seems inapplicable in such situations. In this paper, we show that the Moore-Penrose generalized inverse of a singular FIM can be interpreted as the CRB corresponding to the minimum variance among all choices of minimum constraint functions. This result ensures the logical validity of applying the Moore-Penrose generalized inverse of an FIM as the covariance lower bound when the FIM is singular. Furthermore, the result can be applied as a performance bound on the joint design of constraint functions and unbiased estimators.
Funding Games: the Truth but not the Whole Truth
Venue: arXiv cs.GT 2012
Year: 2012

We introduce the Funding Game, in which $m$ identical resources are to be allocated among $n$ selfish agents. Each agent requests a number of resources $x_i$ and reports a valuation $\tilde{v}_i(x_i)$, which verifiably {\em lower}-bounds $i$'s true value for receiving $x_i$ items. The pairs $(x_i, \tilde{v}_i(x_i))$ can be thought of as size-value pairs defining a knapsack problem with capacity $m$. A publicly-known algorithm is used to solve this knapsack problem, deciding which requests to satisfy in order to maximize the social welfare. We show that a simple mechanism based on the knapsack {\it highest ratio greedy} algorithm provides a Bayesian Price of Anarchy of 2, and for the complete information version of the game we give an algorithm that computes a Nash equilibrium strategy profile in $O(n^2 \log^2 m)$ time. Our primary algorithmic result shows that an extension of the mechanism to $k$ rounds has a Price of Anarchy of $1 + \frac{1}{k}$, yielding a graceful tradeoff between communication complexity and the social welfare.
Matching Pursuits with Random Sequential Subdictionaries
Venue: arXiv cs.DS 2012
Year: 2012

Matching pursuits are a class of greedy algorithms commonly used in signal processing, for solving the sparse approximation problem. They rely on an atom selection step that requires the calculation of numerous projections, which can be computationally costly for large dictionaries and burdens their competitiveness in coding applications. We propose using a non adaptive random sequence of subdictionaries in the decomposition process, thus parsing a large dictionary in a probabilistic fashion with no additional projection cost nor parameter estimation. A theoretical modeling based on order statistics is provided, along with experimental evidence showing that the novel algorithm can be efficiently used on sparse approximation problems. An application to audio signal compression with multiscale time-frequency dictionaries is presented, along with a discussion of the complexity and practical implementations.
Strategic delegation in a sequential model with multiple stages
Venue: arXiv cs.GT 2012
Year: 2012

We analyze strategic delegation in a Stackelberg model with an arbitrary number, n, of firms. We show that the n-1 last movers delegate their production decisions to managers whereas the first mover does not. Equilibrium incentive rates are increasing in the order with which managers select quantities. Letting u_i^* denote the equilibrium payoff of the firm whose manager moves in the i-th place, we show that u_n^*>u_{n-1}^*>...>u_2^*>u_1^*. We also compare the delegation outcome of our game with that of a Cournot oligopoly and show that the late (early) moving firms choose higher (lower) incentive rates than the Cournot firms.
Complex Orthogonal Designs with Forbidden $2 \times 2$ Submatrices
Venue: arXiv cs.IT 2012
Year: 2012

Complex orthogonal designs (CODs) are used to construct space-time block codes. COD $\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p \times n$ matrix, where nonzero entries are filled by $\pm z_i$ or $\pm z^*_i$, $i = 1, 2,..., k$, such that $\mathcal{O}^H_z \mathcal{O}_z = (|z_1|^2+|z_2|^2+...+|z_k|^2)I_{n \times n}$. Define $\mathcal{O}_z$ a first type COD if and only if $\mathcal{O}_z$ does not contain submatrix {\pm z_j & 0; \ 0 & \pm z^*_j}$ or ${\pm z^*_j & 0; \ 0 & \pm z_j}$. It is already known that, all CODs with maximal rate, i.e., maximal $k/p$, are of the first type. In this paper, we determine all achievable parameters $[p, n, k]$ of first type COD, as well as all their possible structures. The existence of parameters is proved by explicit-form constructions. New CODs with parameters $[p,n,k]=[\binom{n}{w-1}+\binom{n}{w+1}, n, \binom{n}{w}], $ for $0 \le w \le n$, are constructed, which demonstrate the possibility of sacrificing code rate to reduce decoding delay. It's worth mentioning that all maximal rate, minimal delay CODs are contained in our constructions, and their uniqueness under equivalence operation is proved.
Securing Tor Tunnels under the Selective-DoS Attack
Venue: arXiv cs.CR 2012
Year: 2012

Anonymous communication systems are subject to selective denial-of-service (DoS) attacks. Selective DoS attacks lower anonymity as they force paths to be rebuilt multiple times to ensure delivery which increases the opportunity for more attack. In this paper we present a detection algorithm that filters out compromised communication channels for one of the most widely used anonymity networks, Tor. Our detection algorithm uses two levels of probing to filter out potentially compromised tunnels. We perform probabilistic analysis and extensive simulation to show the robustness of our detection algorithm. We also analyze the overhead of our detection algorithm and show that we can achieve satisfactory security guarantee for reasonable communication overhead (5% of the total available Tor bandwidth in the worst case). Real world experiments reveal that our detection algorithm provides good defense against selective DoS attack.
Prescient Precoding in Heterogeneous DSA Networks with Both Underlay and Interweave MIMO Cognitive Radios
Venue: arXiv cs.IT 2012
Year: 2012

This work examines a novel heterogeneous dynamic spectrum access network where the primary users (PUs) coexist with both underlay and interweave cognitive radios (ICRs); all terminals being potentially equipped with multiple antennas. Underlay cognitive transmitters (UCTs) are allowed to transmit concurrently with PUs subject to interference constraints, while the ICRs employ spectrum sensing and are permitted to access the shared spectrum only when both PUs and UCTs are absent. We investigate the design of MIMO precoding algorithms for the UCT that increase the detection probability at the ICRs, while simultaneously meeting a desired Quality-of-Service target to the underlay cognitive receivers (UCRs) and constraining interference leaked to PUs. The objective of such a proactive approach, referred to as prescient precoding, is to minimize the probability of interference from ICRs to the UCRs and primary receivers due to imperfect spectrum sensing. We begin with downlink prescient precoding algorithms for multiple single-antenna UCRs and multi-antenna PUs/ICRs. We then present prescient block-diagonalization algorithms for the MIMO underlay downlink where spatial multiplexing is performed for a plurality of multi-antenna UCRs. Numerical experiments demonstrate that prescient precoding by UCTs provides a pronounced performance gain compared to conventional underlay precoding strategies.
Scaling Inference for Markov Logic with a Task-Decomposition Approach
Venue: arXiv cs.AI 2012
Year: 2012

Motivated by applications in large-scale knowledge base construction, we study the problem of scaling up a sophisticated statistical inference framework called Markov Logic Networks (MLNs). Our approach, Felix, uses the idea of Lagrangian relaxation from mathematical programming to decompose a program into smaller tasks while preserving the joint-inference property of the original MLN. The advantage is that we can use highly scalable specialized algorithms for common tasks such as classification and coreference. We propose an architecture to support Lagrangian relaxation in an RDBMS which we show enables scalable joint inference for MLNs. We empirically validate that Felix is significantly more scalable and efficient than prior approaches to MLN inference by constructing a knowledge base from 1.8M documents as part of the TAC challenge. We show that Felix scales and achieves state-of-the-art quality numbers. In contrast, prior approaches do not scale even to a subset of the corpus that is three orders of magnitude smaller.
On Berry's conjectures about the stable order in PCF
Venue: arXiv cs.LO 2012
Year: 2012

PCF is a sequential simply typed lambda calculus language. There is a unique order-extensional fully abstract cpo model of PCF, built up from equivalence classes of terms. In 1979, Gérard Berry defined the stable order in this model and proved that the extensional and the stable order together form a bicpo. He made the following two conjectures: 1) "Extensional and stable order form not only a bicpo, but a bidomain." We refute this conjecture by showing that the stable order is not bounded complete, already for finitary PCF of second-order types. 2) "The stable order of the model has the syntactic order as its image: If a is less than b in the stable order of the model, for finite a and b, then there are normal form terms A and B with the semantics a, resp. b, such that A is less than B in the syntactic order." We give counter-examples to this conjecture, again in finitary PCF of second-order types, and also refute an improved conjecture: There seems to be no simple syntactic characterization of the stable order. But we show that Berry's conjecture is true for unary PCF. For the preliminaries, we explain the basic fully abstract semantics of PCF in the general setting of (not-necessarily complete) partial order models (f-models.) And we restrict the syntax to "game terms", with a graphical representation.
Generalized Louvain Method for Community Detection in Large Networks
Venue: arXiv cs.SI 2012
Year: 2012

In this paper we present a novel strategy to discover the community structure of (possibly, large) networks. This approach is based on the well-know concept of network modularity optimization. To do so, our algorithm exploits a novel measure of edge centrality, based on the k-paths. This technique allows to efficiently compute a edge ranking in large networks in near linear time. Once the centrality ranking is calculated, the algorithm computes the pairwise proximity between nodes of the network. Finally, it discovers the community structure adopting a strategy inspired by the well-known state-of-the-art Louvain method (henceforth, LM), efficiently maximizing the network modularity. The experiments we carried out show that our algorithm outperforms other techniques and slightly improves results of the original LM, providing reliable results. Another advantage is that its adoption is naturally extended even to unweighted networks, differently with respect to the LM.
Multi-agent Robust Consensus: Convergence Analysis and Application
Venue: arXiv cs.DC 2012
Year: 2012

The paper investigates consensus problem for continuous-time multi-agent systems with time-varying communication graphs subject to process noises. Borrowing the ideas from input-to-state stability (ISS) and integral input-to-state stability (iISS), robust consensus and integral robust consensus are defined with respect to $L_\infty$ and $L_1$ norms of the disturbance functions, respectively. Sufficient and/or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus, which answer the question: how much communication capacity is required for a multi-agent network to converge despite certain amount of disturbance. The $ε$-convergence time is then obtained for the network as a special case of the robustness analysis. The results are based on quite general assumptions on switching graph, weights rule and noise regularity. In addition, as an illustration of the applicability of the results, distributed event-triggered coordination is studied.
Exact Reconstruction Conditions for Regularized Modified Basis Pursuit
Venue: arXiv cs.IT 2012
Year: 2012

In this correspondence, we obtain exact recovery conditions for regularized modified basis pursuit (reg-mod-BP) and discuss when the obtained conditions are weaker than those for modified-CS or for basis pursuit (BP). The discussion is also supported by simulation comparisons. Reg-mod-BP provides a solution to the sparse recovery problem when both an erroneous estimate of the signal's support, denoted by $T$, and an erroneous estimate of the signal values on $T$ are available.
Inapproximability of Orthogonal Compaction
Venue: arXiv cs.CG 2012
Year: 2012

We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in polynomial time unless P = NP. We also provide a fixed-parameter-tractable algorithm for testing whether a drawing can be compacted to a small number of rows.
Private Decayed Sum Estimation under Continual Observation
Venue: arXiv cs.DS 2012
Year: 2012

In monitoring applications, recent data is more important than distant data. How does this affect privacy of data analysis? We study a general class of data analyses - computing predicate sums - with privacy. Formally, we study the problem of estimating predicate sums {\em privately}, for sliding windows (and other well-known decay models of data, i.e. exponential and polynomial decay). We extend the recently proposed continual privacy model of Dwork et al. We present algorithms for decayed sum which are $\eps$-differentially private, and are accurate. For window and exponential decay sums, our algorithms are accurate up to additive $1/\eps$ and polylog terms in the range of the computed function; for polynomial decay sums which are technically more challenging because partial solutions do not compose easily, our algorithms incur additional relative error. Further, we show lower bounds, tight within polylog factors and tight with respect to the dependence on the probability of error.
ATP and Presentation Service for Mizar Formalizations
Venue: arXiv cs.DL 2012
Year: 2012

This paper describes the Automated Reasoning for Mizar (MizAR) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of MizAR services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles.
LWE-based Identification Schemes
Venue: arXiv cs.CR 2012
Year: 2012

Some hard problems from lattices, like LWE (Learning with Errors), are particularly suitable for application in Cryptography due to the possibility of using worst-case to average-case reductions as evidence of strong security properties. In this work, we show two LWE-based constructions of zero-knowledge identification schemes and discuss their performance and security. We also highlight the design choices that make our solution of both theoretical and practical interest.
A deterministic algorithm for fitting a step function to a weighted point-set
Venue: arXiv cs.DS 2012
Year: 2012

Given a set of n points in the plane, each point having a positive weight, and an integer k>0, we present an optimal O(n \log n)-time deterministic algorithm to compute a step function with k steps that minimizes the maximum weighted vertical distance to the input points. It matches the expected time bound of the best known randomized algorithm for this problem. Our approach relies on Cole's improved parametric searching technique.
Improved Distance Oracles and Spanners for Vertex-Labeled Graphs
Venue: arXiv cs.DS 2012
Year: 2012

Consider an undirected weighted graph G=(V,E) with |V|=n and |E|=m, where each vertex v is assigned a label from a set L of \ell labels. We show how to construct a compact distance oracle that can answer queries of the form: "what is the distance from v to the closest lambda-labeled node" for a given node v in V and label lambda in L. This problem was introduced by Hermelin, Levy, Weimann and Yuster [ICALP 2011] where they present several results for this problem. In the first result, they show how to construct a vertex-label distance oracle of expected size O(kn^{1+1/k}) with stretch (4k - 5) and query time O(k). In a second result, they show how to reduce the size of the data structure to O(kn \ell^{1/k}) at the expense of a huge stretch, the stretch of this construction grows exponentially in k, (2^k-1). In the third result they present a dynamic vertex-label distance oracle that is capable of handling label changes in a sub-linear time. The stretch of this construction is also exponential in k, (2 3^{k-1}+1). We manage to significantly improve the stretch of their constructions, reducing the dependence on k from exponential to polynomial (4k-5), without requiring any tradeoff regarding any of the other variables. In addition, we introduce the notion of vertex-label spanners: subgraphs that preserve distances between every node v and label lambda. We present an efficient construction for vertex-label spanners with stretch-size tradeoff close to optimal.
Various complexity results for computational mass spectrometry problems
Venue: arXiv cs.CC 2012
Year: 2012

Define Minimum Soapy Union (MinSU) as the following optimization problem: given a $k$-tuple $(X_1, X_2,..., X_k)$ of finite integer sets, find a $k$-tuple $(t_1, t_2,..., t_k)$ of integers that minimizes the cardinality of $(X_1 + t_1) \cup (X_2 + t_2) \cup ... \cup (X_n + t_k)$. We show that MinSU is NP-complete, APX-hard, and polynomial for fixed $k$. MinSU appears naturally in the context of protein shotgun sequencing: Here, the protein is cleaved into short and overlapping peptides, which are then analyzed by tandem mass spectrometry. To improve the quality of such spectra, one then asks for the mass of the unknown prefix (the shift) of the spectrum, such that the resulting shifted spectra show a maximum agreement. For real-world data the problem is even more complicated than our definition of MinSU; but our intractability results clearly indicate that it is unlikely to find a polynomial time algorithm for shotgun protein sequencing.
Approximation Algorithms for Variable-Sized and Generalized Bin Covering
Venue: arXiv cs.DS 2012
Year: 2012

We consider the Generalized Bin Covering (GBC) problem: We are given $m$ bin types, where each bin of type $i$ has profit $p_i$ and demand $d_i$. Furthermore, there are $n$ items, where item $j$ has size $s_j$. A bin of type $i$ is covered if the set of items assigned to it has total size at least the demand $d_i$. In that case, the profit of $p_i$ is earned and the objective is to maximize the total profit. To the best of our knowledge, only the cases $p_i = d_i = 1$ (Bin Covering) and $p_i = d_i$ (Variable-Sized Bin Covering (VSBC)) have been treated before. We study two models of bin supply: In the unit supply model, we have exactly one bin of each type, i.\,e., we have individual bins. By contrast, in the infinite supply model, we have arbitrarily many bins of each type. Clearly, the unit supply model is a generalization of the infinite supply model. To the best of our knowledge the unit supply model has not been studied yet. Our results for the unit supply model hold not only asymptotically, but for all instances. This contrasts most of the previous work on \prob{Bin Covering}. We prove that there is a combinatorial 5-approximation algorithm for GBC with unit supply, which has running time $\bigO{nm\sqrt{m+n}}$. Furthermore, for VSBC we show that the natural and fast Next Fit Decreasing ($\NFD$) algorithm is a 9/4-approximation in the unit supply model. The bound is tight for the algorithm and close to being best-possible. We show that there is an AFPTAS for VSBC in the \emph{infinite} supply model.
Innocent strategies as presheaves and interactive equivalences for CCS (expanded version)
Venue: arXiv cs.LO 2012
Year: 2012

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of 'plays', and a subcategory V of 'views'. We argue that presheaves on V adequately represent 'innocent' strategies, in the sense of game semantics. We equip innocent strategies with a simple notion of interaction. We then prove decomposition results for innocent strategies, and, restricting to presheaves of finite ordinals, prove that innocent strategies are a final coalgebra for a polynomial functor derived from the game. This leads to a translation of CCS with recursive equations. Finally, we propose a notion of 'interactive equivalence' for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework, we consider analogues of fair testing and must testing. We show that must testing is strictly finer in our model than in CCS, since it avoids what we call 'spatial unfairness'. Still, it differs from fair testing, and we show that it coincides with a relaxed form of fair testing.